The Anaphora was indeed studied by Rome and held to validly effect Eucharistic Consecration, despite the absence of an explicit Institution Narrative. However no Chaldean parishes use the Anaphora of Holy Addai and Mari without including explicit Words of Institution, nor are they permitted to do so, or likely to be so permitted in the immediate future. Additionally, as matters stand, doing so would be counter to their liturgical tradition, as they lack the matter associated with the ability to offer the Anaphore without the Institution Text.
At the time of the union of the Chaldeans with Rome, there was a requirement stated that the explicit Words were to be inserted into the Anaphora. While this is often looked at as merely a latinization, there are those who consider it to have also been an acknowledgement of the fact that the Chaldeans would be cut off from a historical Assyrian usage - the Sacrament of the Holy Leaven or Malka - not infrequently advanced to explain why there was not considered a need for an Institutional Narrative.
No Assyrian priest may bake Eucharistic Bread without adding Malka (Holy Leaven) to the mixture. Malka consists of a tiny amount of the last previously consecrated Eucharist and tradition holds that the use of Malka traces, unbroken, to a piece of the Eucharistic Bread reserved by the Apostle John at the Last Supper, passed on to Thomas (spiritual father to the Assyrian Church), and thence to Holy Addai and Mari.
Chaldeans lack this Eucharistic “starter” and will, until such time as union is achieved with their Sister Church.